Consider a system with $2$ types of resources: A and B$.$ The maximum resources that can be allocated to each process and the current allocation are as follows:

$$ Maximum Resources:

$$ Process P$1$: A$=6,$ B$=5$

$$ Process P$2$: A$=3,$ B$=2$

$$ Process P$3$: A$=7,$ B$=4$

$$ Currently Allocated Resources:

$$ Process P$1$: A$=2,$ B$=1$

$$ Process P$2$: A$=1,$ B$=0$

$$ Process P$3$: A$=0,$ B$=2$

Assume the system has $8$ units of A and $6$ units of B available initially. Use the Banker's Algorithm to answer the following questions:

$1.$ Is the system in a safe state initially? If yes, provide a safe sequence. If no$,$ explain why not.

$2.$ If Process P$2$ requests resources A$=2,$ B$=2,$ can the request be granted

immediately? Explain your answer.

$3.$ If Process P$3$ requests resources A$=3,$ B$=1,$ can the request be granted

immediately? Explain your answer